Multistability refers to the capacity of a system to operate at several discrete, alternative stable steady-states, and is one of the most important features of biological dynamics. The phenomenon of multistability, which is the focus of much modern biomedical. research, is found at all scales, from the molecular and cellular, to tissues, organisms, populations, and ecosystems. In order to understand the role played by some of these interactions (for example the role of a gene regulatory network or a signaling pathway in a cell), one often faces great difficulties in trying to interpret the effect of positive and negative feedbacks, nonlinear interactions, and other complex signaling between the nodes of the biological interaction network. We propose to develop new theory and to significantly expand existing theory for understanding multistability in biological interaction networks, and identifying the key features of biological interaction networks that give rise to multistable behavior. Also, we will create software that implements our various existing multistability-related algorithms, and any newly discovered methods that result form this work. To guide and complement our theoretical work, we will investigate whether our mathematical techniques lead to predictions which can be validated experimentally. The long-term goal of the proposed work is to analyze multistability as a fundamental theoretical concept that traverses levels of biological complexity, and to develop theoretical, computational, and experimental tools to understand multistability in concrete biological interaction networks. Understanding multistability in gene regulatory networks and signaling pathways will play an important role in the study of key cellular processes deregulated during carcinogenesis. The analysis of multistability will also benefit research in cellular differentiation (relevant to tissue engineering), viral infections (e.g. HIV's dormant state), and the immune system. Our software tools and our experimental genetic systems will be made available to the biomedical research community.